Activity in the portions of the brain connected with social perception was tracked for a sample of university students, and the number of Facebook friends was recorded for the same sample. (From R. Kanai, B. Bahrami, R. Roylance, G. Rees, “Online social network size is reflected in human brain structure,” Proceedings of the Royal Society B, Published online http://rspb.royalsocietypublishing.org/content/early/2011/10/12/ rspb.2011.1959.full)
Review the data in Brain-Facebook.xls, then
(a) Plot the two variables in a scatterplot.
(b) The metric used for GM density is complex to some extent and it is not necessary to understand it for the purposes of this exercise. However, looking at the scale for GM density, make a guess at how those numbers were calculated. Hint: Review Section 4.4.
(c) Calculate the correlation between brain activity and Facebook friends.
(d) Test whether it is statistically significant and interpret the results.
(e) What is the hypothesized direction of causality? Is this direction confirmed by the results of the hypothesis test?